s251ex2(fa10) - MATH 251 Exam II November 8, 2010 ANSWER...

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Unformatted text preview: MATH 251 Exam II November 8, 2010 ANSWER KEY (Form A) 1. C 2, D 3. A 4. A 5. C 6. B 7. (a) F 8. (a) spiral point, (c) node, (e) improper node, 9. (a) f (t) = 1 − 2te−t 3 (b) f (t ) = u 9 (t ) − e −3t + 27 cos(4t − 36) + e −3t + 27 sin( 4t − 36) 2 10. y (t ) = 11. (b) G (c) D U U U (d) A (b) proper node (star point), A (d) center, S 7 −t 3 − 3t 11 1 e − e + u 6 (t ) e −t + 6 − − e −3t + 18 2 2 36 2 2 7 1 1 − 3t 2t (a) x(t ) = C1 e + C 2 e (b) saddle point, unstable (c) β = −14 12. (a) Substitute (2, 2) into the equations directly to see that x′ = y′ = 0. (b) (0, 0) and (−2, −2) (c) saddle point, unstable. ...
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This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.

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